ABSTRACT
The aim of this paper is to study the efficiency and robustness of adaptive techniques and goal-oriented error estimates for a benchmark test. The techniques used here are based on a simple post-process of the finite element approximations. The goal-oriented error estimates are obtained by analyzing the direct problem and an auxiliary problem related to a specific quantity of interest. The proposed procedure is valid for both linear and non-linear quantities. Different error representations are discussed and the influence of the dispersion error is analyzed. The numerical results show that the error estimates provide fairly good approximations of the actual error and that the proposed adaptive refinement technique leads to a faster reduction of the error.
Keywords:
error estimates; goal-oriented adaptivity; Benchmark Test
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